Factors

# Factors of 172 | Prime Factorization of 172 | Factor Tree of 172

Written by Prerit Jain

Updated on: 18 Aug 2023

Contents

### Factors of 172 | Prime Factorization of 172 | Factor Tree of 172

Factors of 172 | Factor Pairs of 172 | Prime factors of 172 |
---|---|---|

172 = 1, 2, 4, 43, 86, 172 | (1, 172), (2, 86), (4, 43) | 172 = 2 × 43 |

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**What are the factors of 172**

If you have a big number, 172. Do you know all the numbers can be multiplied together and given back the original big number? These interesting numbers are called factors and they make it easy for us to do tricky multiplication problems! How can find out the factors:

Start dividing our big number (172) by each of the integers between 1 and 172 until none of them leave any number behind after division. That means if our answer isn’t an even whole number then there was something left over – so that integer wouldn’t work as one of the factors needed to equal 172 which is graphically illustrated below;

______1______2____4___43__ 86_172

Divide ->|_____/\________/\___/\/X____ / \________________| X = Remainder != 0 | No match! | Match Found! |

In the above example 2(86), 4(43), 43(4), & 86(2) worked – for 1 & 172 their quotients or answers gave exact matches without leaving a reminder — then these too must be counted as successful divisions made in searching through potential factors Lastly, multiplying each factor yields results in exactly the original figure: i.e., 88 x 2 = 176 thus resulting in another potential factor.

**How to Find Factors of 172**

Four different methods that to find the factors of 124:

Factors of 124 using Multiplication Method

Factors of 124 using the Division Method

Prime Factorization of 124

Factor tree of 124

**Factors of 172 using Multiplication Method**

Factors can appear a bit tricky for you. But, don’t worry! We have a solution to easily find all the factors of any given number – including 172!

Consider our 172, and start with 1 as one of its potential factors, then it’s just like telling us “how many times will 1 go into getting this number?”. Then let’s try 2 – how many times does it fit in there? And go on with this for other numbers too till you find the highest factor- in this case being 86×2=172. Thus these are all possible combinations resulting from multiplying together numbers between 1 and 172:

1 x 172 = 172; 2 x 86 = 172; 4 x 43 = 172. So using the multiplication method, we conclude that when multiplied correctly equation results in the original value (elements such as operators play a part here also) meaning those elements combined make up a set of 6 values called “factors” or divisors:1,2,4,43,86 & 172.

**Factors of 172 Using Division Method**

Ever curious to know what numbers when multiplied together give a certain result? Come on! We can find out the factors of any number by Division Method.

Let’s try it with 172. To find out all the factors, we need to divide 172 by every single counting number from 1 up until itself (in this case, also 172). So that would mean dividing by one first:

• Anything number divided by 1 will always give us back our original number thus both 1 and 172 are already going on our list of possibilities –

Next, let’s see for 2 and 4 :

• If your results have no remainder then you got yourself another factor pairing – which brings us 86 for 2 x 43 = 86 and 43 for 4 x 43=43. Keep it up!

And finally, let’s check 172/86 &172/172, shall we?:

• Seeing as these divisions leave nothing but zero behind when rounded off, now we can evidently see how each pair of these makes up different combinations resulting away with six total factors: 1(1×172),2 (2*86),4 (4×43 ),43(43×4),86 (86 ×2)!

**Prime Factorization of 172**

Prime factorization breaks down a number into pieces and those pieces are called its ‘prime factors’.

To find the prime factors for 172, we are now using a factor tree.

A factor tree shows how to break up one big number by using smaller numbers that have been multiplied together.

We’ll start with 172 kept at the top of our diagram, then draw branches for all its divisors – 2. Since 86 can be divided by two equals 43 we’ll write “86” on the branch below 2 and divide again until we get 4 as a result of dividing 43 by itself.

So finally the Factor Tree gives the Prime Factors of 172 as 2 x 2 x 43

**Factor Pairs of 172**

What are factor pairs? For a number like 172, if you take two different numbers and multiply them together to get the original number, those numbers result in the factor pair combinations for your given number. So let’s try out some examples:

1×172 = 172 ; 2×86=172; 43×4 =172. By testing all these combinations between 1 and 172, we can find an outcome totaling back up with 172. In this example resulting as :

(1,172)

(2,86)

(4,43).

**Factors of 172 – Quick Recap**

**Factors of 172:** 1, 2, 4, 43, 86, 172

**Negative Factors of 172:** -1, -2, -4, -43, -86, -172.

**Prime Factors of 172:** 2 × 43

**Prime Factorization of 172:** 2 × 43

**Fun Facts of Factors of 172**

The number 172 is exciting! Being made by two consecutive numbers, 8 and 22 (8×22=172). It is special because unlike usual numbers 170 results in not only a simple outcome but also a number actually made up of its prime factors when multiplied by two whole numbers together (i.e) 2 x 4 x 43 = 172 – hence no other combination will work as well to make this sum. Plus there are seven distinct factors in total for this number: 1,2, 4, 8,43 86 & 172! Pretty cool right? Did you know it’s also equal to four consecutive prime numbers added together? 41 + 43 + 47+ 53 = 174 What an amazing little numeral huh?!

**Examples of Factor of 172**

1. What is the prime factorization of 172?

Answer: The prime factorization of 172 is 2 x 2 x 43.

2. What are the factors of 172?

Answer: The factors of 172 are 1, 2, 4, 43, 86, and 172.

3. Is 172 a composite number?

Answer: Yes, 172 is a composite number because it has more than two factors (1, 2, 4, 43, 86, and 172).

4. Are there any square numbers in the factors of 172?

Answer: Yes square number 4 can be found in the factors of 172.

5. Is there a relationship between the factors of 172 and its prime factorization?

Answer: Yes, the prime factorization of 172 (2 x 2 x 43) tells us that all its factors must be divisible by either 2 or 43, or 1. Therefore all the factors of 172 are divisible by either 2 or 43 or 1.

6. How many odd numbers appear in the factors of 172?

Answer: 2 odd numbers appear in the factors of 172 which are 1, 43

7 . Are there any even numbers in the list of factors for 172?

Answer: Yes, four even numbers appear in the list of factors for 172 which are 2,4,86 and 172.

8 . What do we call numbers whose only two factors are themselves and one?

Answer: Numbers whose only two factors are themselves and one are called prime numbers.

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**Frequently Asked Questions**

### What is the prime factorization of 172?

Answer: The prime factorization of 172 is 2 x 2 x 43.

### What are the factors of 172?

Answer: The factors of 172 are 1, 2, 4, 43, 86, and 172.

### Is 172 a composite number?

Answer: Yes, 172 is a composite number because it has more than two factors (1, 2, 4, 43, 86, and 172).

### Are there any square numbers in the factors of 172?

Answer: Yes 4 is a square number which can be found in the factors of 172.

### Is there a relationship between the factors of 172 and its prime factorization?

Answer: Yes, the prime factorization of 172 (2 x 2 x 43) tells us that all its factors must be divisible by either 2 or 43, or 1. Therefore all the factors of 172 are divisible by either 2 or 43 or 1.

### How many odd numbers appear in the factors of 172?

2 odd number appears in the factors of 172 which are 1 and 43

### Are there any even numbers in the list of factors of 172?

Yes, four even numbers appear in the list of factors for 172 which are 2, 4, 86, and 172.

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Written by by

Prerit Jain